Question

How do I evaluate ∫(13x2+12x−2)dx?

Answer 1

$Given \\ \int(13x^2+12x\ -\ 2)dx \\ we\ know\ that\ \int x^n dx=\frac{x^{n+1}}{n+1}+C \\ =\int 13x^2 dx+\int 12x dx\ -\ \int 2 dx \\ =13\frac{x^{2+1}}{2+1}+12\frac{x^{1+1}}{1+1}\ -\ 2\frac{x^{0+1}}{0+1}+C \\ =13\frac{x^3}{3}+12\frac{x^2}{2}\ -\ 2\frac{x^1}{1} + C \\ \bold{\int(13x^2+12x-2)dx=\frac{13}{3}x^3+6x^2-2x+C}$
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